Interior Magnet Machine With Non-Perpendicular Slots

ABSTRACT

An interior permanent magnet machine having angled slots.

FIELD OF THE INVENTION

The present invention generally relates to machines with permanentmagnets buried in the rotor core and, in particular, slotted rotors forinterior magnet machines operating at variable frequencies under anelectronic control or operating at a fixed frequency.

BACKGROUND OF THE INVENTION

Interior magnet machines have the following characteristics.

First, many interior magnet machines have lower power density thansurface mounted magnet machines. The surface area of the magnet isusually reduced when buried, requiring a larger motor or generator toobtain the same output power. The larger size motor or generator cancause packaging or performance problems in the final application.

Second, a trapezoidal air-gap flux distribution is usually generated bya interior magnet rotor. In applications where the winding currents aresinusoidal, the trapezoidal flux distribution results in significanttorque ripple. The torque ripple contributes to noise and vibration inthe final application. This can be minimized by selection of the correctslot and pole number, but this solution is not always practical.

Third, the abrupt transitions in the rotor flux distribution contributeto cogging torque. Techniques typically used to reduce cogging torque,such as skewing, result in lower power density.

Fourth, interior magnet machines have higher average inductance thansurface magnet machines. The higher inductance reduces the power factorof the machine during operation, increasing the complex power (VA)required from the drive to produce a given output torque. Increasing thedrive volt-ampere requirement can increase the drive cost if largerpower devices must be used.

The output torque of an interior permanent magnet machine isproportional to the back-emf and winding current when the two are inphase. The winding current in a fixed bus voltage system is limited bythe back-emf and machine resistance and inductance. A rotor geometrythat results in higher back-emf or lower inductance allows the number ofturns to be adjusted to obtain minimum current draw. The decrease incurrent may allow for the use of smaller power devices, reducing systemcost.

Prior art solutions for interior magnet machines with power densitygreater than or equal to surface magnet machines include “V” magnet andspoke magnet designs. The designs can be difficult to magnetize and tendto have high cogging torque.

Prior art solutions for reducing the impact of a trapezoidal rotor fluxdistribution include machines with distributed windings. Stators withdistributed windings tend to be larger than single tooth windings due tothe end coils, and may not fit in the package required by someapplications. Single tooth windings in which the number of electricaldegrees per slot is not equal to 120 or 240 can also be used. The numberof practical combinations is limited by the size of the machine.

Prior art solutions for reducing the cogging torque include shaping ofthe stator and rotor air-gap surfaces and skew. These solutions tend toreduce the power density of the machine.

Prior art solutions for reducing the average inductance of a interiormagnet machine include adding slits to the rotor pole cap. These slitsare placed perpendicular to the magnet surface in most cases.

SUMMARY OF THE INVENTION

Other objects and features will be in part apparent and in part pointedout hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1, 2, 3, 6, 9, 10, 14, 15, and 16 are cross sectional views ofembodiments of the invention including four interior magnets, eachhaving two angled slots per magnetic pole.

FIG. 1A is a graph illustrating the back emf of a motor or generatorincluding a rotor having laminations as illustrated in FIG. 1 includingangled slots 16.

FIG. 1B is a graph illustrating the back emf of a motor or generatorincluding a rotor having laminations as illustrated in FIG. 1 withoutangled slots 16.

FIGS. 2A, 3A, 6A, 9A, 10A, 14A, and 15A are graphs illustrating the backemf of a motor or generator including a rotor having laminations asillustrated in FIGS. 2, 3, 6, 9, 10, 14, and 15, respectively, eachincluding angled slots.

FIGS. 4, 5, 7, 8, 11, 12, and 13 are cross sectional views ofembodiments of the invention including four interior magnets, eachhaving four angled slots per magnetic pole.

FIGS. 4A, 5A, 7A, 8A, 11A, 12A, and 13A are graphs illustrating the backemf of a motor or generator including a rotor having laminations asillustrated in FIGS. 4, 5, 7, 8, 11, 12, and 13, respectively, eachincluding angled slots.

FIG. 9B is a graph illustrating the cogging torque of a motor orgenerator including a rotor having laminations as illustrated in FIG. 9including angled slots 172.

FIG. 11B is a graph illustrating the cogging torque of a motor orgenerator including a rotor having laminations as illustrated in FIG. 11including angled slots 202.

FIGS. 17 and 18 are cross sectional views of embodiments of theinvention including six interior magnets, each having two angled slotsper magnetic pole.

FIGS. 19 and 20 are cross sectional views of embodiments of theinvention including two interior magnets, each having two angled slotsper magnetic pole.

FIG. 19A is a graph illustrating the flux distribution of a motor orgenerator including a rotor having laminations as illustrated in FIG. 19including angled slots 364.

FIG. 19B is a graph illustrating the flux density distribution of amotor or generator including a rotor having laminations as illustratedin FIG. 19 including angled slots 364.

FIG. 21 is a cross sectional view of an embodiment of the inventionincluding twelve interior magnets, arranged to produce six magneticpoles with two angled slots per pole.

FIG. 22 is a cross sectional view of a crown rotor lamination of theprior art without any angled slots according to the invention. Thecrowning of the pole surface results in a non-uniform air-gap.

FIG. 22A is a graph illustrating the back emf of a non-uniform air-gapmotor or generator including a rotor having laminations as illustratedin FIG. 22 according to the prior art without any angled slots.

FIG. 22B is a graph illustrating the cogging torque of a non-uniformair-gap motor or generator including a rotor having laminations asillustrated in FIG. 22 according to the prior art without any angledslots.

Corresponding reference characters indicate corresponding partsthroughout the drawings.

DETAILED DESCRIPTION OF THE INVENTION

In one embodiment, the invention comprises a machine having a stator anda rotor in magnetic coupling engagement with the stator, wherein therotor has a geometry with angled slots between the magnet surface andthe rotor outside diameter. In another embodiment, the inventioncomprises a rotor geometry with slots added between the magnet surfaceand the rotor outside diameter. The slots are placed at an angle and ina location that can increase the fundamental component of the rotor fluxdistribution. The slots may also decrease the cogging torque. A minimumof two slots per magnetic pole are added. Although any even number ofslots is illustrated by the embodiments herein, those skilled in the artwill recognize other configurations.

The addition of the slots changes the rotor flux distribution from atrapezoidal shape to a more sinusoidal distribution. The fundamentalcomponent of the more sinusoidal distribution can be greater than thefundamental component of the trapezoidal distribution, and the harmonicdistortion of the distribution can be reduced. Appendix 1 is amathematical construction of the invention. The first section shows theuniform (trapezoidal) rotor flux distribution without the slots. The FFTfundamental component of the flux distribution is 1.433 amplitude units.The total harmonic distortion of the distribution is 11.805%. The nextsection of Appendix 1 present a method for calculating the location ofthe slots. The method presented increases the fundamental component to1.616 and reduces the THD to 4.263%.

FIGS. 1-21 show a possible implementation of the slots that match thematch the mathematical model above. Appendix 2 and FIGS. 19A and 19Bshow the rotor flux distribution for the rotor in FIG. 19 with andwithout the slots, as predicted by finite element analysis. Thefundamental component of the flux increases by 5.6% with the slot added.The FEA model also shows a significant reduction in the total harmonicdistortion of the flux distribution. Note the mathematical model doesnot account for leakage around the slot.

A comparison of the mathematical model and FEA model can be made usingthe rotor shown in FIG. 17. This rotor has a reduced leakage path. TheFEA model predicts an 11.5% increase in the fundamental flux versus a12.7% increase predicted by the mathematical model.

The FEA model shows improvement in the shape of the flux distribution,the magnitude of the fundamental component of the flux distribution,average inductance, back-emf fundamental component magnitude, coggingtorque magnitude, average torque, and torque ripple.

The location and angle of the slots have not been optimized at thistime. Further work is required to optimize these parameters for torqueproduction and cogging torque reduction.

The advantages described above also apply to line start permanent magnetmachines. Examples of LSPM rotors are in FIGS. 19 and 20. The angles andlocations of the slots may need to be adjusted due to the presence ofthe cage.

The invention reduces the cogging torque while maintaining or increasingthe back-emf and average torque production. This is a highly unusualresult. Most methods used for reducing cogging torque also reduce theback-emf and average torque.

The higher back-emf can be taken advantage of in two ways. First, it canbe used to increase the power density of the machine, by increasing thetorque supplied by a fixed motor or generator size, or by reducing thesize of the motor or generator to produce the same torque.

Alternatively, the number of turns could be reduced to keep the sameback-emf. The inductance of the machine is proportional to the square ofthe turns, so a substantial reduction in inductance is possible. A motoror generator using the rotor shown in FIG. 1 with the slots produces1.9% more torque than a rotor without the slots. Assuming the torque isproportional to the number of turns, reducing the number of turns by1.9% to produce the same torque with the slots results in a 3.76%decrease in the average inductance.

FIGS. 1-21 illustrate various embodiments of the invention. Forconvenience, the rotor of the invention is illustrated in cross sectionas a lamination having slots. In use, the stack of laminations would befitted with permanent magnets and the slots would be open (i.e., airfilled) or filled with a non-magnetic material. For convenience, eachlamination is illustrated as including the interior permanent magnets.

Thus, FIG. 1 is an exemplary illustration of one embodiment of a rotoraccording to the invention. The rotor includes a cylindrical periphery18 having a central axis of rotation 10. The cross-section of the rotor,as shown in FIG. 1, is taken perpendicular to the central axis 10 andincludes the following. A plurality of buried (e.g., interior) permanentmagnets 14 are positioned with slots in the rotor, each magnet 14 havinga longitudinal dimension which is greater than a transverse dimension(e.g., rectangular in cross section). A plurality of non-magnetic slots16 are associated with one of the magnets 14, each slot 16 having alongitudinal dimension which is greater than a transverse dimension,wherein an axis of the longitudinal dimension of the slot is notperpendicular to an axis of the longitudinal dimension of its associatedinterior magnet. Each slot 24 is positioned generally between theperiphery 18 and one of the interior magnets 14 with which the slot 24is associated. Preferably, there are an even number of at least twoslots 24 associated with each magnetic pole. An axis of the longitudinaldirection of each magnet 14 is substantially parallel to a tangent ofthe periphery 18 of the cylindrical housing. In one embodiment, theslots 16 are at an angle not equal to 90 degrees relative to the axis ofthe longitudinal dimension of its associated interior magnet 14.

FIG. 1 is a cross sectional view taken along a perpendicular to acentral axis of rotation 10 of a lamination 12 of a rotor according toone embodiment of the invention. Each interior magnet 14 has twoassociated slots 16 between the magnet 14 and a periphery 18 of thelamination wherein the longitudinal axis 20 of the slots are at an angleof less than 90 degrees relative to a longitudinal axis 22 of itsassociated interior magnet 14. In this embodiment, each interior magnet14 has optional end slots 24. The slots 16 and/or the end slots 24 maybe filled with air or other non-magnetic material.

In FIGS. 2-16, various lamination embodiments are illustrated, eachhaving four identical quadrants as shown with regard to quadrants A, B,C and D of FIG. 1. For simplicity, only one quadrant is described andlabeled with reference characters.

FIG. 2 is a cross sectional view taken along a perpendicular to thecentral axis of rotation 10 of a lamination 30 of a rotor according toone embodiment of the invention similar to FIG. 1. In this embodiment,the longitudinal axis 32 of the slots 34 are at a greater angle (butless than 90 degrees) relative to a longitudinal axis 36 of itsassociated interior magnet 38 as compared to the angle of axis 20illustrated in FIG. 1. In this embodiment, the slots 32 are shorter inlength than the slots 16 of FIG. 1.

FIG. 3 is a cross sectional view taken along a perpendicular to the axisof rotation 10 of a lamination 50 of a rotor according to one embodimentof the invention similar to FIG. 1. In this embodiment, the longitudinalaxis 52 of the slots 54 are at a lesser angle (but greater than 0degrees and less than 90 degrees) relative to a longitudinal axis 56 ofits associated interior magnet 58 as compared to the angle of axis 20 ofthe slots 16 illustrated in FIG. 1. In this embodiment, the slots 54 arelonger in length than the slots 16 of FIG. 1.

FIG. 4 is a cross sectional view taken along a perpendicular to the axisof rotation 10 of a lamination 72 of a rotor according to one embodimentof the invention.

Each interior magnet 74 has four associated slots 76 and 77 between themagnet 74 and a periphery 78 of the lamination wherein the longitudinalaxis 80 and 81 of the slots are at an angle of less than 90 degreesrelative to a longitudinal axis 82 of its associated interior magnet 74.In this embodiment, each interior magnet 74 has optional slotted ends 84which may be filled with air or other non-magnetic material. In thisembodiment, the two outer slots 76 form a smaller angle with the axis 82than the two inner slots 77 and the two outer slots 76 are shorter inlength than the two inner slots 77.

FIG. 5 is a cross sectional view taken along a perpendicular to the axisof rotation 10 of a lamination 92 of a rotor according to one embodimentof the invention. Each interior magnet 94 has four associated slots 96and 97 between the magnet 94 and a periphery 98 of the laminationwherein the longitudinal axis 100 and 101 of the slots are at an angleof less than 90 degrees relative to a longitudinal axis 102 of itsassociated interior magnet 94. In this embodiment, each interior magnet94 has optional slotted ends 104 which may be filled with air or othernon-magnetic material. In this embodiment, the two outer slots 96 formthe same angle with the axis 102 than the two inner slots 97 and the twoouter slots 96 are shorter in length than the two inner slots 97.

FIG. 6 is a cross sectional view taken along a perpendicular to the axisof rotation 10 of a lamination 110 of a rotor according to oneembodiment of the invention similar to FIG. 1. In this embodiment, thelongitudinal axis 112 of the slots 114 are at the same angle relative toa longitudinal axis 116 of its associated interior magnet 118 ascompared to the angle illustrated of FIG. 1. In this embodiment, theslots 114 are the same length as the slots 16 of FIG. 1. In thisembodiment, the longitudinal axis 113 of the slots 115 are at a lesserangle relative to a longitudinal axis 116 of its associated interiormagnet 118 as compared to the angle of axis 20 of the slots 16illustrated in FIG. 1. In this embodiment, the slots 115 are longer inlength than the slots 16 of FIG. 1.

FIG. 7 is a cross sectional view taken along a perpendicular to the axisof rotation 10 of a lamination 132 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 5except that slots 134 have a longitudinal axis 136 which isperpendicular relative to a longitudinal axis 138 of its associatedinterior magnet 140.

FIG. 8 is a cross sectional view taken along a perpendicular to the axisof rotation 10 of a lamination 152 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 5except that slots 154 have a longitudinal axis 156 which is at a lesserangle relative to a longitudinal axis 158 of its associated interiormagnet 160 as compared to the angle of axis 101 of slots 97 of FIG. 5.

FIG. 9 is a cross sectional view taken along a perpendicular to the axisof rotation 10 of a lamination 170 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 1except that slots 172 are tear-shaped having one end which is wider thanthe other end as compared to the slots 16 of FIG. 1. In addition, theslots 172 have a longitudinal axis 174 which is at a lesser anglerelative to a longitudinal axis 176 of its associated interior magnet178 as compared to the angle of axis 20 of the slots 16 of FIG. 1.

FIG. 10 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 180 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 1except that end slots 182 are narrower in width than the end slots 24 ofFIG. 1.

FIG. 11 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 200 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 4except that slots 202 are tear-shaped having one end which is wider thanthe other end as compared to the slots 76 of FIG. 4. In addition, theslots 202 have a longitudinal axis 204 which is at a lesser anglerelative to a longitudinal axis 206 of its associated interior magnet208 as compared to the angle of axis 80 of the slots 76 of FIG. 4.

FIG. 12 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 220 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 11except that slots 222 have a narrower width as compared to the slots 202of FIG. 11. In addition, the slots 222 have a longitudinal axis 224which is at a greater angle relative to a longitudinal axis 226 of itsassociated interior magnet 228 as compared to the angle of axis 204 ofthe slots 202 of FIG. 11.

FIG. 13 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 240 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 12except that slots 242 have a longitudinal axis 244 which is at a lesserangle relative to a longitudinal axis 246 of its associated interiormagnet 248 as compared to the angle of axis 224 of the slots 222 of FIG.12.

FIG. 14 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 260 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 1except that one of two slots 262, namely slot 262B, is longer andtear-shaped as compared to the slots 16 of FIG. 1, both of which are thesame shape and position. In addition, the tear-shaped slot 262B has alonger length along axis 264B as compared to the slots 16 of FIG. 1. Inaddition, slot 262B is at a lesser angle relative to a longitudinal axis266 of its associated interior magnet 268 as compared to the angle ofaxis 20 of the slots 16 of FIG. 1.

FIG. 15 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 280 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 1except that both slots 282 are tear-shaped and slot 282B is longer ascompared to the slots 16 of FIG. 1, both of which are the same shape andposition. In addition, the tear-shaped slot 282B has a longer lengthalong axis 284B as compared to the slots 16 of FIG. 1. In addition, bothtear-shaped slots 282 are at a lesser angle relative to a longitudinalaxis 286 of its associated interior magnet 288 as compared to the angleof axis 20 of slots 16 of FIG. 1.

FIG. 16 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 290 of a rotor according to oneembodiment of the invention. This embodiment is the same as FIG. 1except that both slots 292 are connected to a slot 294 for an associatedinterior magnet 296 as compared to FIG. 1 wherein the slots 16 are notconnected to the slots for magnets 14. In addition, both slots 292 areat a lesser angle relative to a longitudinal axis 298 of its associatedinterior magnet 296 as compared to the angle of axis 20 of slots 16 ofFIG. 1.

FIG. 17 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 300 of a rotor according to oneembodiment of the invention. FIG. 17 is similar to FIG. 1 except that ithas six interior magnets 302 instead of the four interior magnets 14 ofFIG. 1. In addition, FIG. 17 has S-shaped slots 304 instead of the slots16 of FIG. 1, which are generally shaped rectangular with roundedcorners.

FIG. 18 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 340 of a rotor according to oneembodiment of the invention. In FIG. 18, six interior magnets 342equally spaced about the periphery are illustrated. Each magnet has atrapezoidal end slot 344 at each end. Each interior magnet 342 has twoassociated slots 346 between the magnet 342 and a periphery 348 of thelamination 340 and wherein the longitudinal axis 350 of the slots 346are at an angle of less than 90 degrees relative to a longitudinal axis352 of its associated interior magnet 342. In this embodiment, eachinterior magnet 342 is illustrated as having the optional end slots 344.The slots 346 and/or the end slots 344 may be filled with air or othernon-magnetic material. In addition, as illustrated in FIG. 18, the slots346 are not connected to one of the end slots 344. Further, in thisembodiment, the at least part of the end slots 344 have an axis 354which is coaxial with a radius 356 of the lamination 340.

FIG. 19 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 360 of a rotor according to oneembodiment of the invention. In FIG. 19, two parallel interior magnets362 equally spaced within the periphery are illustrated. Each interiormagnet 362 has two associated slots 364 between the magnet 362 andstarting cage slots 366 positioned about the periphery 368 of thelamination 360. The longitudinal axis 370 of the slots 364 are at anangle of less than 90 degrees relative to a longitudinal axis 372 of itsassociated interior magnet 362. The slots 364 and/or the starting cageslots 366 may be filled with air or other non-magnetic material. Inaddition, as illustrated in FIG. 19, the slots 364 are connected to andintegral with one of the starting cage slots 366.

FIG. 20 is a cross sectional view taken along a perpendicular to theaxis of rotation 10 of a lamination 380 of a rotor according to oneembodiment of the invention. FIG. 20 is the same as FIG. 19 except slots382 are not connected to any of starting cage slots 384. Instead, inFIG. 20, the slots 382 are independent of the cage slots 384 and arepositioned between the cage slots 384 and magnets 386.

FIG. 21 is a cross sectional view taken along a perpendicular to acentral axis of rotation 10 of a lamination 400 of a rotor according toone embodiment of the invention. In FIGS. 1-20 above, the interiormagnets are positioned parallel to a tangent to the periphery of therotor lamination. In contrast, in the lamination 400 of FIG. 21 eachinterior magnet 402R, 402L is part of a V-shaped pair and each is at anangle relative to the tangent to the periphery. Further, each magnet402R, 402L has at least one associated slot 404R, 404L between themagnet 402R, 402L and a periphery 406 of the lamination. In thisembodiment, a longitudinal axis 408R, 408L of the slots 404R, 404L areat an angle of less than 90 degrees relative to a longitudinal axis410R, 410L of its associated interior magnet 402.

In the embodiment of FIG. 21, the longitudinal axis 408R, 408L of eachslot 404R, 404L is not coaxial with a radius 412 of the lamination 400,although it is contemplated that the axis 408R, 408L and radius 412 maybe coaxial. Similarly, in FIG. 1-20, the slots are not coaxial with aradius because the interior magnets are positioned parallel to a tangentto the periphery of the rotor lamination and the slots are paired, witheach slot of a pair facing the other slot of the pair. Thus, the slotsform an angle of less than 90 degrees with the interior magnets. It iscontemplated that the slots may face away from each other in which casethe slots may be coaxial with a radius of the rotor but the slots wouldstill be at an angle of less than 90 degrees with the interior magnets.

FIG. 22 is an illustration of a crown rotor according to the prior artwithout any slots. Each interior magnet 420 has an end slot 422, asshown. The end slots of FIGS. 1-18 have a slightly different shape thanthe end slots 422. In particular, the end slots of FIGS. 1-18 werepositioned to be the same distance from the periphery as the end slots422 to maintain the same flux leakage. A stator 430 is shown in phantom,the stator being in magnetic coupling arrangement with the crown rotor.

TABLE 1 illustrates finite element modeling results regarding the backemf and cogging for the embodiments of FIGS. 1, 2, 3, 4, 5 and 22 havingthe slot dimensions indicated. Slot 1 refers to the slots in a two slotconfiguration and the outer slots in a four slot configuration. Slot 2refers to the inner slots of a four slot configuration.

TABLE 2 illustrates finite element modeling results regarding the backemf and cogging for the embodiments of FIGS. 6, 7, 8, 9, 10 and 11having the slot dimensions indicated. Slot 1 refers to the slots in atwo slot configuration and the outer slots in a four slot configuration.Slot 2 refers to the inner slots of a four slot configuration.

TABLE 3 illustrates finite element modeling results regarding the backemf and cogging for the embodiments of FIGS. 12, 13, 14 and 15 havingthe slot dimensions indicated. Slot 1 refers to the slots in a two slotconfiguration and the outer slots in a four slot configuration. Slot 2refers to the inner slots of a four slot configuration.

TABLE 4 illustrates test results regarding the back emf and cogging forthe embodiments of FIGS. 1, 9, 11 and 22 (CROWN) having the slotdimensions indicated. TABLE 1 FIGS. 1, 2, 3, 4, 5 AND 22. Crown W/OSLOTS Back-EMF Fundamental V_(pk) at 0.105 0.106 0.109 0.109 0.109 0.1090.109 2 rpm 5th Harmonic % Fund. 0.04 2.52 1.62 1.68 1.8 1.62 1.66 7thHarmonic % Fund. 0.64 1.22 1.62 1.36 1.79 1.6 1.6 11th Harmonic % Fund.2.65 8.53 11.38 11.47 5.93 11.31 10.43 13th Harmonic % Fund. 0.09 0.593.66 2.76 3.35 3.57 2.82 THD % 0.09 0.86 1.48 1.51 0.69 1.47 1.21Cogging Nm_(pk) 0.085 0.377 0.085 0.377 0.208 0.083 0.06 Pole Arc edeg158.94 158.94 158.94 158.94 158.94 158.94 Slot 1 Dimensions InnerTangent Arc edeg N/A N/A 111.8 111.8 111.8 111.8 111.8 Inner Radius mmN/A N/A 0.75 0.75 0.75 0.75 0.75 Outer Tangent Arc edeg N/A N/A 87.7697.36 78.16 87.76 87.76 Outer Radius mm N/A N/A 0.75 0.75 0.75 0.75 0.75Slot 2 Dimensions Inner Tangent Arc edeg N/A N/A N/A N/A N/A 40.88 53.4Inner Radius mm N/A N/A N/A N/A N/A 0.75 0.75 Outer Tangent Arc edeg N/AN/A N/A N/A N/A 23.36 23.36 Outer Radius mm N/A N/A N/A N/A N/A 0.750.75

TABLE 2 FIGS. 6, 7, 8, 9, 10 AND 11. Back-EMF Fundamental V_(pk) at0.108 0.108 0.108 0.109 0.107 0.105 2 rpm 5th Harmonic % Fund. 2.24 1.791.68 1.62 1.73 1.91 7th Harmonic % Fund. 1.56 1.26 1.63 1.68 2.08 1.6111th Harmonic % Fund. 1.84 9.63 9.24 9.77 8.64 6.16 13th Harmonic %Fund. 5.93 0.33 1.43 1.57 2.83 0.43 THD % 0.5 1.01 0.94 1.05 0.9 0.48Cogging Nm_(pk) 0.354 0.386 0.086 0.024 0.13 0.096 Pole Arc edeg 158.94158.94 158.94 158.94 162 158.94 Slot 1 Dimensions Inner Tangent Arc edeg111.8 111.8 111.8 111.8 111.8 Inner Radius mm 0.75 0.75 0.75 0.75 0.75Outer Tangent Arc edeg 100.06 87.76 87.76 87.76 87.76 Outer Radius mm0.75 0.75 1.5 0.75 1.5 Slot 2 Dimensions Inner Tangent Arc edeg 53.453.4 N/A N/A 53.4 Inner Radius mm 0.75 0.75 N/A N/A 0.75 Outer TangentArc edeg 23.36 18.36 N/A N/A 18.36 Outer Radius mm 0.75 0.75 N/A N/A0.75

TABLE 3 FIGS. 12, 13, 14 AND 15. Back-EMF Fundamental V_(pk) at 0.1070.105 0.107 0.104 2 rpm 5th Harmonic % Fund. 1.73 1.82 2.71 2.75 7thHarmonic % Fund. 1.62 1.6 0.95 0.63 11th Harmonic % Fund. 8.16 7.12 8.4812.59 13th Harmonic % Fund. 1.03 0.709 5.74 1.98 THD % 0.74 0.59 1.211.73 Cogging Nm_(pk) 0.068 0.082 0.295 0.232 Pole Arc edeg 158.94 158.94158.4 158.4 Slot 1 Dimensions Inner Tangent Arc edeg 111.8 111.8 111.8111.8 Inner Radius mm 0.75 0.75 0.75 0.75 Outer Tangent Arc edeg 87.7687.76 87.76 87.76 Outer Radius mm 1.125 1.125 0.75 1.5 Slot 2 DimensionsInner Tangent Arc edeg 53.4 59.92 114.48 111.8 Inner Radius mm 0.75 0.750.75 0.75 Outer Tangent Arc edeg 18.36 18.36 40.28 26.04 Outer Radius mm0.75 0.75 1.5 1.5

TABLE 4 FIGS. 1, 9, 11 AND 22 Crown W/O Back-EMF SLOTS Maximum V_(pk) at51.1 57.3 62.6 58.1 53.1 1000 rpm Fundamental V_(pk) at 50.9 53.5 54.853.4 50.5 1000 rpm 5th Harmonic % Fund. 0.75 1.84 0.93 1.01 1.19 7thHarmonic % Fund. 0.42 0.76 1.18 1.23 1.1 11th Harmonic % Fund. 2.22 7.9311.34 9.18 5.28 13th Harmonic % Fund. 0.14 1.2 3.58 1.28 1.09 THD %0.059 0.729 1.46 0.903 0.341 Cogging Nm_(pk) 0.086 0.281 0.037 0.0340.031

Having described the invention in detail, it will be apparent thatmodifications and variations are possible without departing from thescope of the invention defined in the appended claims.

When introducing elements of the present invention or the preferredembodiments(s) thereof, the articles “a”, “an”, “the” and “said” areintended to mean that there are one or more of the elements. The terms“comprising”, “including” and “having” are intended to be inclusive andmean that there may be additional elements other than the listedelements.

In view of the above, it will be seen that the several objects of theinvention are achieved and other advantageous results attained.

As various changes could be made in the above constructions, products,and methods without departing from the scope of the invention, it isintended that all matter contained in the above description and shown inthe accompanying drawings shall be interpreted as illustrative and notin a limiting sense.

Appendix 1—Mathematical Construction

IPM Flux Concentration

The torque produced by an electric machine results from the interactionof the stator and rotor magnetic fields. The majority of the torque isproduced by the fundamental component of each field. For the interiorpermanent magnet rotor shown in FIG. 1, the rotor air-gap flux waveshapeshown in FIG. 2 is typical.

The total flux under the waveform shown is:φ_(r) =A ₁ p ₁  (1)where A₁ is the amplitude of the air-gap flux and p₁ is the width of theflux waveform as a percentage of a pole pitch. The fundamental componentof the air-gap flux is given by: $\begin{matrix}{b_{1} = {\frac{{- 2}A_{1}}{\pi}\left\{ {{\cos\left\lbrack \frac{\pi\quad\left( {1 + p_{1}} \right)}{2} \right\rbrack} - {\cos\left\lbrack \frac{\pi\quad\left( {1 - p_{1}} \right)}{2} \right\rbrack}} \right\}}} & (2)\end{matrix}$The invention changes the shape of the air-gap waveform so as toincrease the fundamental component. The addition of one set of slots(FIG. 4) changes the rotor air-gap flux distribution to that shown inFIG. 4.

The total rotor air-gap flux remains unchanged since the magnet width,length, and operating conditions have not been changed, orφ_(r) =A ₂ p ₂+(A ₃ −A ₂)p ₃  (3)The fundamental component of this waveform is: $\quad\begin{matrix}{b_{1} = {{\frac{{- 2}A_{2}}{\pi}\left\{ {{\cos\left\lbrack \frac{\pi\quad\left( {1 + p_{3}} \right)}{2} \right\rbrack} - {\cos\left\lbrack \frac{\pi\quad\left( {1 - p_{2}} \right)}{2} \right\rbrack}} \right\}} - {\frac{2A_{3}}{\pi}\left\{ {{\cos\left\lbrack \frac{\pi\quad\left( {1 - p_{2}} \right)}{2} \right\rbrack} - {\cos\left\lbrack \frac{\pi\quad\left( {1 - p_{3}} \right)}{2} \right\rbrack}} \right\}} - {\frac{2A_{2}}{\pi}\left\{ {{\cos\left\lbrack \frac{\pi\left( {1 + p_{2}} \right)}{2} \right\rbrack} - {\cos\left\lbrack \frac{\pi\quad\left( {1 - p_{3}} \right)}{2} \right\rbrack}} \right\}}}} & (4)\end{matrix}$

An example of the increase in the fundamental component due to the slotsis given in Table 1. The flux from the magnets is the same for each ofthe waveforms in the example, since the area under the waveforms is 1.0in each case. The fundamental component increases by 12.8%. The increasein the fundamental component of the air-gap flux results in greaterback-emf and torque. The change in the air-gap flux distribution, asindicated by the change in total harmonic distortion, will also changethe cogging torque. TABLE 1 FIG. 2 Waveform FIG. 4 Waveform A1 1.149 —p1 0.87 — A2 — 0.6 p2 — 0.87 A3 — 1.596 p3 — 0.48 Area Under Waveform1.0 1.0 Fundamental 1.433 1.616 Total Harm. Distortion (%) 11.803 4.263The analysis above ignores motor non-linearity, stator slotting effects,and flux leakage. Each of these will affect the analysis above. Somemodification of slot position is necessary to account for these effects.

Appendix 2 Rotor Flux Distribution

FFT of Air-Gap Flux Distribution Calculation by Finite Element

Takes fourier transform of flux density versus angle waveform.

Read Data from Files

no_slot:=READPRN(“c:\projects:flux_focus\fea_slotflux_dist__s

slot:=READPRN(“c:\projectsflux_focus\feaflux_dist_sl”)

Extract Data from Files

1. A rotor comprising: a cylindrical periphery having a central axis ofrotation; a cross-section taken perpendicular to the central axisincluding: a plurality of interior permanent magnets, each magnet havinga longitudinal dimension which is greater than a transverse dimension; aplurality of non-magnetic slots, each slot associated with one of themagnets, each slot having a longitudinal dimension which is greater thana transverse dimension, wherein an axis of the longitudinal dimension ofthe slot is not perpendicular to an axis of the longitudinal dimensionof its associated interior magnet.
 2. The rotor of claim 1 wherein eachslot positioned generally between the periphery and one of the interiormagnets with which the slot is associated
 3. The rotor of claim 1wherein there are at least two slots associated with each magnetic pole.4. The rotor of claim 4 wherein the slots associated with each magnethave different lengths.
 5. The rotor of claim 1 wherein at least one ofthe slots has at least one of the following shapes: a tear-shape and anS-shape.
 6. The rotor of claim 1 further comprising an additionalnon-magnetic end slot adjacent an end of each interior magnets.
 7. Therotor of claim 1 wherein at least one of slots is integral with a slotfor its associated interior magnet.
 8. The rotor of claim 7 wherein atleast part of the end slots have an axis which is coaxial with a radiusof the rotor.
 9. The rotor of claim 1 further comprising starting cageslots forming an interior starting cage of the rotor.
 10. The rotor ofclaim 10 wherein at least one of the slots is connected to the at leastone of starting cage slots.
 11. The rotor of claim 10 wherein the slotsare positioned between the cage and the magnets.
 12. The rotor of claim1 wherein the magnets have a V-configuration and the slots are coaxialwith a radius of the rotor.
 13. A machine comprising: a stator; and arotor in magnetic coupling engagement with the stator, said rotorcomprising a cylindrical periphery having a central axis of rotation; across-section taken perpendicular to the central axis including: aplurality of buried interior permanent magnets, each magnet having alongitudinal dimension which is greater than a transverse dimension; aplurality of non-magnetic slots, each slot associated with one of themagnets, each slot having a longitudinal dimension which is greater thana transverse dimension, wherein an axis of the longitudinal dimension ofthe slot is not perpendicular to an axis of the longitudinal dimensionof its associated interior magnet.
 14. The machine of claim 14 whereineach slot positioned generally between the periphery and one of theinterior magnets with which the slot is associated
 15. The machine ofclaim 14 wherein there are at least two slots associated with eachmagnetic pole.
 16. The machine of claim 14 wherein at least one of theslots has at least one of the following shapes: a tear-shape and anS-shape.
 17. The machine of claim 14 further comprising an additionalnon-magnetic end slot adjacent an end of each interior magnets.
 18. Themachine of claim 14 wherein at least one of slots is integral with aslot for its associated interior magnet.
 19. The machine of claim 14further comprising starting cage slots forming an interior starting cageof the machine.
 20. The machine of claim 14 wherein the magnets have aV-configuration and the slots are coaxial with a radius of the machine.21. A rotor comprising a plurality of laminations, each having acylindrical periphery having a central axis of rotation; a cross-sectiontaken perpendicular to the central axis including: a plurality ofinterior permanent magnet slots, each magnet slot having a longitudinaldimension which is greater than a transverse dimension; a plurality ofnon-magnetic slots, each non-magnetic slot associated with one of themagnet slots, each non-magnetic slot having a longitudinal dimensionwhich is greater than a transverse dimension, wherein an axis of thelongitudinal dimension of the non-magnetic slot is not perpendicular toan axis of the longitudinal dimension of its associated interior magnetslot.